CN108632043A - A kind of ring signatures method and system of optimization - Google Patents
A kind of ring signatures method and system of optimization Download PDFInfo
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- CN108632043A CN108632043A CN201810354020.7A CN201810354020A CN108632043A CN 108632043 A CN108632043 A CN 108632043A CN 201810354020 A CN201810354020 A CN 201810354020A CN 108632043 A CN108632043 A CN 108632043A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3255—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using group based signatures, e.g. ring or threshold signatures
Abstract
The present invention discloses a kind of ring signatures method and system of optimization.The ring signatures method includes：Obtain each user identity and message to be signed；According to each user identity, parameter is randomly selected, generates systematic parameter and master key；According to the systematic parameter, the master key and the user identity, the corresponding private key of the user identity is determined；According to message, the user identity and the private key corresponding with user identity to be signed, corresponding ring signatures are obtained；Judge whether the ring signatures are effectively to sign.The ring signatures method optimized using the present invention, can improve the communication efficiency of ring signatures.
Description
Technical field
The present invention relates to the communications fields, more particularly to a kind of ring signatures method and system of optimization.
Background technology
Ring signatures system under conventional public-key infrastructure (PKI) frame is faced with two main problems：It is to use first
The management of family public key certificate, under PKI systems, the identity of user is bound with its public key by digital certificate, and number of users is worked as
When measuring huge, management and the verification of certificate will occupy a large amount of system resource, become the bottleneck of whole system application.In ring signatures
In system, this problem is particularly evident, and verifier not only needs to verify the public key certificate of signer, also to verify other use in ring
The public key certificate at family, signer is also required to the certificate of other users in verification ring before signing, to ensure hideing for itself
Name property, when there are many number of users in ring, the efficiency of signature and verification will be all severely impacted.Scholar Shamir was in 1984
Identity- based cryptography is proposed, under this framework, the identity information of user is the public key of user, corresponding private key
It is calculated according to the private key of user identity and system by key generation centre (KGC), due to avoiding in traditional PKI systems
The problem of management of client public key certificate, Identity- based cryptography are got the attention.The ring signatures system of identity-based
It is that ID-based cryptosystem technology is formed with ring signatures technological incorporation, is slightly different with original ring signatures system, is based on body
The ring signatures system tool of part is responsible for the user in system there are one center KGC trusty and generates corresponding public and private key, but KGC
Presence should not influence the anonymities of ring signatures, i.e. it is which user carries out in ring signature that KGC, which can not also be known,.It is so far
Only, although there is a series of identity-based signature scheme on ring signatures scheme and the lattice on lattice, in existing ring signatures scheme
In, main problem concentrates on these aspects still to be improved in terms of the calculating of system, communication efficiency, safety.
Invention content
The object of the present invention is to provide a kind of ring signatures method and system of optimization, can improve the communication effect of ring signatures
Rate.
To achieve the above object, the present invention provides following schemes：
A kind of ring signatures method of optimization, which is characterized in that the ring signatures method includes：
Obtain each user identity and message to be signed；
According to each user identity, parameter is randomly selected, generates systematic parameter and master key；
According to the systematic parameter, the master key and the user identity, the corresponding private key of the user identity is determined；
According to message, the user identity and the private key corresponding with user identity to be signed, obtain corresponding
Ring signatures；
Judge whether the ring signatures are effectively to sign.
Optionally, each user identity of the acquisition and message to be signed, specifically include:
According to two hash functions, multiple user identity ID and message m to be signed are obtained.
Optionally, each user identity of the basis randomly selects parameter, generates systematic parameter and corresponding main
Key specifically includes:
According to each user identity Selecting All Parameters n, trap generating function TrapGen (1 is run according to parameter n, KGCn) generate
One matrixAnd ∧┴(A0) corresponding base S one short0, then calculate,
And enable S0For main private key, (A is enabled0, T) and it is main public keys；
Wherein, (1 TrapGenn) it is trap generating function, the purpose for running the function is one information of output to (A, T),
Here A is statistically to approachOn one be uniformly distributed, T is ∧┴(A) well-founded on, A0It is tieed up for a nxm
Matrix, ID1Indicate the identity ID, ID of first user in ring2Indicate the identity ID of second user in ring, and so on, H0
Indicate hash function, formulaIndicate to calculate each user public keys and.
Optionally, described according to the systematic parameter, the master key and the user identity, determine the user identity
Corresponding private key, specifically includes：
Base is called to delete function BasisDel (A0,H0(IDi),S0, σ) and algorithm obtainsWhereinFor ∧┴(A0(H0
(IDi))-1) andAny one base；
Wherein, BasisDel is that base deletes function, and σ indicates that normal distribution standard difference parameter, function export lattice ∧┴(A0(H0
(IDi))-1) on a random base, and meetWherein A0(H0(IDi))-1The transposition of representing matrix；
To 1≤j≤m, non-homogeneous small integer solution sampling function is calledCome
Generate Sij, wherein tjBe T jth row andIt enablesFor IDiSecret
Key, therefore,And A0(H0(IDi))-1Si=T.
It is optionally, described according to message, the user identity and the private key corresponding with user identity to be signed,
Corresponding ring signatures are obtained, are specifically included：
(a)Wherein,It is the DISCRETE NORMAL distribution on the Zm of σ, y for standard deviation1,y2,…yl
For the feature vector of each User ID；
(b) it calculates
Wherein, y1,y2,…ylIndicate that the syndrome (i.e. feature vector) of each User ID on ring R, μ indicate ring R signatures
Information, c are indicated according to algorithmic formulaCalculated signing messages；
If (c) j=i sets zj=Sic+yj, zj indicate upper j-th of the User ID of ring R feature vector otherwise set zj
=yj, output signature (μ, z1, z2... zl, c, R) probability beR expressions are made of each User ID
Ring,Wherein M indicates that a calculated constant, value are closed with T-phase,Being expressed as standard deviation is
DISCRETE NORMAL distribution on the Zm of σ,It indicates with v ∈ ZmCentered on and vector Z m that standard deviation is σ on DISCRETE NORMAL point
Cloth, l indicate the quantity of user in ring R.
Optionally, described to judge whether the ring signatures are effectively to sign, it specifically includes：
By ring signatures (μ, the z1, z2... zl, c, R) and input following equation：
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl- Tc, μ)=c
Judge whether above-mentioned equation is true；
If above-mentioned equation is set up, the ring signatures are effectively to sign；
If above-mentioned equation is invalid, the ring signatures are invalid signature.
To achieve the above object, the present invention provides following schemes：
A kind of ring signatures system of optimization, the ring signatures system include：
User identity acquisition module, for obtaining each user identity；
Message capturing module to be signed, for obtaining message to be signed；
Systematic parameter, master key acquisition module generate system for according to each user identity, randomly selecting parameter
Parameter of uniting and master key；
Private key acquisition module, for according to the systematic parameter, the master key and the user identity, determining the use
The corresponding private key of family identity；
Ring signatures acquisition module, for according to message, the user identity and the described and user identity pair to be signed
The private key answered obtains corresponding ring signatures；
Judgment module, for judging whether the ring signatures are effectively to sign.
According to specific embodiment provided by the invention, the invention discloses following technique effects：
The present invention discloses a kind of ring signatures method and system of optimization.The ring signatures method includes：Obtain each user
Identity and message to be signed；According to each user identity, parameter is randomly selected, generates systematic parameter and master key；Root
According to the systematic parameter, the master key and the user identity, the corresponding private key of the user identity is determined；It is waited for according to described
Signature information, the user identity and the private key corresponding with user identity, obtain corresponding ring signatures；Judge the ring label
Whether name is effectively to sign.The ring signatures method optimized using the present invention, can improve the communication efficiency of ring signatures.
Description of the drawings
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the present invention
Example, for those of ordinary skill in the art, without having to pay creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the ring signatures method flow diagram of optimization of the embodiment of the present invention；
Fig. 2 is the ring signatures system construction drawing of optimization of the embodiment of the present invention.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of ring signatures method and system of optimization, can improve the communication effect of ring signatures
Rate.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, below in conjunction with the accompanying drawings and specific real
Applying mode, the present invention is described in further detail.
Fig. 1 is the ring signatures method flow diagram of optimization of the embodiment of the present invention.As shown in Figure 1, a kind of ring signatures side of optimization
Method, the ring signatures method include：
Step 101：Each user identity and message to be signed are obtained, is specifically included：According to two hash functions, obtain more
A user identity ID and message m to be signed.
Step 102：According to each user identity, parameter is randomly selected, generates systematic parameter and master key；
Step 103：According to the systematic parameter, the master key and the user identity, the user identity pair is determined
The private key answered；
Step 104：According to message, the user identity and the private key corresponding with user identity to be signed, obtain
To corresponding ring signatures；
Step 105：Judge whether the ring signatures are effectively to sign.
In step 102, each user identity of the basis randomly selects parameter, generates systematic parameter and corresponding
Master key, specifically include:
According to each user identity Selecting All Parameters n, trap generating function TrapGen is run according to parameter n, KGC
(1n) generate a matrixAnd ∧┴(A0) corresponding base S one short0, then calculate,And enable S0For main private key, (A is enabled0, T) based on it is public close
Key；
Wherein, (1 TrapGenn) it is trap generating function, the purpose for running the function is one information of output to (A, T),
Here A is statistically to approachOn one be uniformly distributed, T is ∧┴(A) well-founded on, A0It is tieed up for a nxm
Matrix, ID1Indicate the identity ID, ID of first user in ring2Indicate the identity ID of second user in ring, and so on, H0
Indicate hash function, formulaIndicate to calculate each user public keys and.
It is described according to the systematic parameter, the master key and the user identity in step 103, determine the user
The corresponding private key of identity, specifically includes：
Base is called to delete function BasisDel (A0,H0(IDi),S0, σ) and algorithm obtainsWhereinFor ∧┴(A0(H0
(IDi))-1) andAny one base；
Wherein, BasisDel is that base deletes function, and σ indicates that normal distribution standard difference parameter, function export lattice ∧┴(A0(H0
(IDi))-1) on a random base, and meetWherein A0(H0(IDi))-1The transposition of representing matrix；
To 1≤j≤m, non-homogeneous small integer solution sampling function is called
To generate Sij, wherein tjBe T jth row andIt enablesFor IDiPrivate
Key, therefore,And A0(H0(IDi))-1Si=T.
It is described according to message, the user identity and the private corresponding with user identity to be signed in step 104
Key obtains corresponding ring signatures, specifically includes：
(a)Wherein,It is the DISCRETE NORMAL distribution on the Zm of σ, y for standard deviation1,y2,…yl
For the feature vector of each User ID；
(b) it calculates
Wherein, y1,y2,…ylIndicate that the syndrome (i.e. feature vector) of each User ID on ring R, μ indicate ring R signatures
Information, c are indicated according to algorithmic formulaCalculated signing messages；
If (c) j=i sets zj=Sic+yj, zj indicate upper j-th of the User ID of ring R feature vector otherwise set zj
=yj, output signature (μ, z1, z2... zl, c, R) probability beR is indicated by each User ID group
At ring,Wherein M indicates that a calculated constant, value are closed with T-phase,It is expressed as standard deviation
It is distributed for the DISCRETE NORMAL on the Zm of σ,It indicates with v ∈ ZmCentered on and vector Z m that standard deviation is σ on DISCRETE NORMAL point
Cloth, l indicate the quantity of user in ring R.
In step 105, it specifically includes：
By ring signatures (μ, the z1, z2... zl, c, R) and input following equation：
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl- Tc, μ)=c
Judge whether above-mentioned equation is true；
If above-mentioned equation is set up, the ring signatures are effectively to sign；
If above-mentioned equation is invalid, the ring signatures are invalid signature.
Fig. 2 is the ring signatures system construction drawing of optimization of the embodiment of the present invention.As shown in Fig. 2, a kind of ring signatures system of optimization
System, the ring signatures system include：
User identity acquisition module 201, for obtaining each user identity；
Message capturing module 202 to be signed, for obtaining message to be signed；
Systematic parameter, master key acquisition module 203 are generated for according to each user identity, randomly selecting parameter
Systematic parameter and master key；
Private key acquisition module 204, for according to the systematic parameter, the master key and the user identity, determining institute
State the corresponding private key of user identity；
Ring signatures acquisition module 205, for according to message, the user identity and the described and user identity to be signed
Corresponding private key obtains corresponding ring signatures；
Judgment module 206, for judging whether the ring signatures are effectively to sign.
First, ring signatures schemes most of so far all rely on hard number theoretical question, discrete logarithm and Bilinear map
Equal support technologies, but unfortunately, it is above-mentioned easily to be cracked in the rear quantum epoch based on the cryptographic problem of number theory.
Due to realizing that simple and safety is higher, the cryptographic technique based on lattice is just greatly paid close attention to by people.The present invention proposes
Scheme only use the linear operations such as modular multiplication and Mo Jia, therefore, compared with traditional ring signatures scheme based on number theory, the present invention
The signature scheme of proposition in efficiency advantageously.Second, the efficiency of the signature scheme based on lattice is mainly by public key, private key and label
The factors such as the calculating time in the length of name, lattice dimension, and extraction and signature algorithm determine that the present invention program only needs several
Signature algorithm can be realized in matrix-vector, to embody the advantage in terms of efficiency of the present invention program, has selected to have disclosed hair
Two kinds of more influential ring signatures schemes based on lattice of table are as a comparison, it is known that, public key of the present invention program in generation
All preferable than existing two kinds ring signatures scheme based on lattice in terms of this 3 leading indicators of length, private key length, signature length
It is shorter, thus needed for signing the calculating time is shorter, memory space is less, overall efficiency higher.
Each embodiment is described by the way of progressive in this specification, the highlights of each of the examples are with other
The difference of embodiment, just to refer each other for identical similar portion between each embodiment.For system disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so description is fairly simple, related place is said referring to method part
It is bright.
Principle and implementation of the present invention are described for specific case used herein, and above example is said
The bright method and its core concept for being merely used to help understand the present invention；Meanwhile for those of ordinary skill in the art, foundation
The thought of the present invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not
It is interpreted as limitation of the present invention.
Claims (7)
1. a kind of ring signatures method of optimization, which is characterized in that the ring signatures method includes：
Obtain each user identity and message to be signed；
According to each user identity, parameter is randomly selected, generates systematic parameter and master key；
According to the systematic parameter, the master key and the user identity, the corresponding private key of the user identity is determined；
According to message, the user identity and the private key corresponding with user identity to be signed, corresponding ring label are obtained
Name；
Judge whether the ring signatures are effectively to sign.
2. the ring signatures method of optimization according to claim 1, which is characterized in that described to obtain each user identity and wait for
Signature information specifically includes:
According to two hash functions, multiple user identity ID and message m to be signed are obtained.
3. the ring signatures method of optimization according to claim 2, which is characterized in that each user's body of the basis
Part, parameter is randomly selected, systematic parameter and corresponding master key is generated, specifically includes:
According to each user identity Selecting All Parameters n, trap generating function TrapGen (1 is run according to parameter n, KGCn) generate one
MatrixAnd ∧┴(A0) corresponding base S one short0, then calculate,
And enable S0For main private key, (A is enabled0, T) and it is main public keys；
Wherein, (1 TrapGenn) it is trap generating function, the purpose for running the function is one information of output to (A, T), here A
Statistically to approachOn one be uniformly distributed, T is ∧┴(A) well-founded on, A0For the square of nxm dimensions
Battle array, ID1Indicate the identity ID, ID of first user in ring2Indicate the identity ID of second user in ring, and so on, H0It indicates
Hash function, formulaIndicate to calculate each user public keys and.
4. the ring signatures method of optimization according to claim 3, which is characterized in that described according to the systematic parameter, institute
Master key and the user identity are stated, the corresponding private key of the user identity is determined, specifically includes：
Base is called to delete function BasisDel (A0,H0(IDi),S0, σ) and algorithm obtainsWhereinFor ∧┴(A0(H0(IDi))-1)
WithAny one base；
Wherein, BasisDel is that base deletes function, and σ indicates that normal distribution standard difference parameter, function export lattice ∧┴(A0(H0
(IDi))-1) on a random base, and meetWherein A0(H0(IDi))-1The transposition of representing matrix；
To 1≤j≤m, non-homogeneous small integer solution sampling function is calledTo generate
Sij, wherein tjBe T jth row andIt enablesFor IDiPrivate key,
Therefore,And A0(H0(IDi))-1Si=T.
5. according to the ring signatures method of the optimization described in claim 4, which is characterized in that described according to the message to be signed, institute
User identity and the private key corresponding with user identity are stated, corresponding ring signatures is obtained, specifically includes：
(a)Wherein,It is the DISCRETE NORMAL distribution on the Zm of σ, y for standard deviation1,y2,…ylIt is each
The feature vector of User ID；
(b) it calculates
Wherein, y1,y2,…ylIndicate that the syndrome (i.e. feature vector) of each User ID on ring R, μ indicate the information of ring R signatures,
C is indicated according to algorithmic formulaCalculated signing messages；
If (c) j=i sets zj=Sic+yj, zj indicate upper j-th of the User ID of ring R feature vector otherwise set zj=yj,
Output signature (μ, z1, z2... zl, c, R) probability beR expressions are made of each User ID
Ring,Wherein M indicates that a calculated constant, value are closed with T-phase,It is σ to be expressed as standard deviation
Zm on DISCRETE NORMAL distribution,It indicates with v ∈ ZmCentered on and standard deviation be σ vector Z m on DISCRETE NORMAL distribution,
L indicates the quantity of user in ring R.
6. according to the ring signatures method of the optimization described in claim 5, which is characterized in that described to judge whether the ring signatures are to have
Effect signature, specifically includes：
By ring signatures (μ, the z1, z2... zl, c, R) and input following equation：
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2…+A0H0(IDl)-1zl-Tc,μ)=c judges whether above-mentioned equation is true；
If above-mentioned equation is set up, the ring signatures are effectively to sign；
If above-mentioned equation is invalid, the ring signatures are invalid signature.
7. a kind of ring signatures system of optimization, which is characterized in that the ring signatures system includes：
User identity acquisition module, for obtaining each user identity；
Message capturing module to be signed, for obtaining message to be signed；
Systematic parameter, master key acquisition module generate system ginseng for according to each user identity, randomly selecting parameter
Number and master key；
Private key acquisition module, for according to the systematic parameter, the master key and the user identity, determining user's body
The corresponding private key of part；
Ring signatures acquisition module, for according to the message to be signed, the user identity and described corresponding with user identity
Private key obtains corresponding ring signatures；
Judgment module, for judging whether the ring signatures are effectively to sign.
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| CN109831306A (en) * | 2019-01-15 | 2019-05-31 | 如般量子科技有限公司 | Anti- quantum calculation ring signatures method and system based on multiple pool of keys |
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| CN102684885A (en) * | 2012-05-25 | 2012-09-19 | 孙华 | Identity-based threshold ring signature method |
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| US9660813B1 (en) * | 2012-03-27 | 2017-05-23 | EMC IP Holding Company LLC | Dynamic privacy management for communications of clients in privacy-preserving groups |
| CN102684885A (en) * | 2012-05-25 | 2012-09-19 | 孙华 | Identity-based threshold ring signature method |
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